-8(b+3) what is the answer

If Mr. Jackson has a circular garden with a diameter of 10 feet surrounded by edging and using the same length of edging, he is going to create a square garden, then the maximum side length of the square is equal to 7.85 feet.

First, we have to find the amount of edging Mr. Jackson has. This can be calculated by finding the circumference.

Circumference can be found by using diameter by the formula;

c = π (diameter)

c = π (10)

c = 3.416 feet

This is the amount of edging on the circular garden. As he has to use the same amount of edging on the square garden, the edging on the square garden is the parameter of the square garden. As the parameter of the square is four times the side length, therefore;

3.416 ÷ 4 = 7.85

Hence, the maximum side length of the square is equal to 7.85 feet.

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According to the question, the given expression is written as below:

The expression is : [tex](\frac{2x^{4} }{10y^{-2} } )(\frac{5y^{3} }{4x^{3} } )[/tex]

Using indices concept, the same variables get cancelled with each other. The divisible numbers get divided by their respective numbers.

And finally, the negative power becomes positive in numerator. Using these concepts the above expression can be re-written as:

Final expression: [tex]\frac{xy^{5} }{y4} =xy[/tex]

Hence, the evaluated expression is [tex]xy[/tex].

What is indices?

In mathematics, the indices are the power or the exponent which is either raised to numbers or variables.

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After rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

The removal of a radical or imaginary number from the denominator of an algebraic fraction is referred to as rationalization. That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

Rationalizing the divisor suggests that you get eliminate the novel within the divisor. 

by the rules of radicals, We can rephrase this as √(5x) / √(2y)

The expression will then be multiplied by √(2y) / √(2y).  Keep in mind that this results in 1, and multiplying this by the first expression has no effect on the original issue.

On multiplying we get-

[√(3x) * √(2y)] / [√(2y) * √(2y)]

[√6xy)] / 2y 

Therefore, after rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

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We get the composite function for the relationship between area and time as A = π (16t + r )².

We are given that, the wave travels at a rate of 16 feet / sec when George jumps off a tire swing in the circular pond.

So, this means that the radius of the wave increases by 16 feet in every second.

Now, we know that, the area of circle is given by:

A = π r²

Now, r increases by 16 feet every second.

So, the composite function will become:

A = π (16t + r )²

where 16 t represents the increase in area in t seconds.

Therefore, we get the composite function for the relationship between area and time as A = π (16t + r )².

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If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

Given:

Angle of depression (∅) = 48°

Opposite side = 871 feet

Let x represent the horizontal distance

Hence,

tan 48° =871/x

x = 871/tan 48°

x= 871/ tan(0.8377)

x= 871/ 1.1106125

x =784.25 feet

Therefore If from the observation deck of a skyscraper, Ian measures a 48∘ angle of depression to a ship in the harbor below. If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

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Answer:

$2,009

Step-by-step explanation:

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The scores from least to greatest is -8. -6, 4, 7

The absolute value of the scores from least to greatest is 4, 6, 7, 8

A negative number is a number that is less than zero. Negative numbers are denoted with a minus sign in front of the number. The further away from zero a negative number is, the smaller the number. Examples of negative numbers are -2, -9.

A positive number is a number that is greater than zero. The further away from zero a positive number is, the greater the number. Examples of negative numbers are 2, 9.

The scores from least to greatest is: -8. -6, 4, 7

The absolute value of a number is when the negative signs from the numbers are removed.

The absolute value of the scores from least to greatest is: 4, 6, 7, 8

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Answer:

here to help!

Step-by-step explanation:

no; Sample answer: If the vertices of ABC are A(1, 2), B(3, 4), and. C(1, 4), then the vertices of the final image are A"(-3, −1), B"(-5, 1), and C"(-3, 1).

For line segment CD, we have that:

10. The length is of 5 units.

12. The midpoint is of (0.5,0).

14. The slope is of -4/3.

The endpoints are given as follows:

c(-1,2) and d(2,-2).

The length is given by the distance between the two endpoints, hence:

[tex]CD = \sqrt{(2 - (-1))^2+(-2-2)^2}[/tex]

CD = sqrt(25) = 5.

The length is of 5 units.

The midpoint is the mean of the coordinates, hence:

The midpoint is (0.5,0).

The slope, taking two points, is given by change in y divided by change in x, hence:

m = (-2 - 2)/(2 - (-1)) = -4/3.

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The value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)

The definition of the functions are given as

f(x) = 4x + 1

g(x) = x^2 - 5

The composite function is given as

(g/f)(x)

The composite function is calculated using

(g/f)(x) = g(x)/f(x)

Substitute the known values in the above equation

So, we have

(g/f)(x) = (x^2 - 5)/(4x + 1)

Hence, the value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)

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The simplified expression after solving the given equation is 8.4721 .

The given expression is,

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex]                                                                   equation 1

Name the given expression as equation 1.

To simplify the given expression first we need to solve step wise,

As we know [tex]\sqrt{7}[/tex] = 2.6457 , we can write,

4[tex]\sqrt{7}[/tex] = 4 × (2.6457) = 10.5830

[tex]\sqrt[3]{7}[/tex] = 1.9129

Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 10.5830 - 1.9129

On further simplifying, we will get

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 8.4721

Thus we can write that the simplified expression after solving the given equation is 8.4721.

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The error that Eli made is that C. He did not solve the equation completely since there are two positive solutions.

It should be noted that the equation given is g² = 49.

In this case, Eli solved it and got -7. This is incorrect.

It should be noted that the appropriate solution should have been ✓49 = 7.

Therefore, the error that Eli made is that C. He did not solve the equation completely since there are two positive solutions.

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The slope can be found as the quotient or rise/run.

Rise - difference of y-coordinates of two points, run - difference of x-coordinates of same two points.

Find the slope using the first two pairs of coordinates in the table:

The y-intercept is the point of intersection of the line with the y-axis.

This point has x = 0 coordinate. On the table we can see the corresponding y- coordinate is  - 2:

The equation of the line is obtained by substituting the values of m and b into slope-intercept form:

The slope is 1/3 and the y-intercept is -2, so the equation is:

y = (1/3)*x - 2

if we use the first two pairs on the table we get:

(-3, -3) and (0, -2)

Then the slope of the linear relation will be:

a = (-2 - (-3))/(0  - (-3)) = (-2 + 3)/3 = 1/3

The slope is 1/3.

We can see that the point (0, -2) is on the table, so the y-intercept is y = -2

How to write the equation?

The linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Then we will get:

y = (1/3)*x - 2

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The midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

It follows from the task content that the midpoint of the line segment joining the two points (-3, 8) and (-8, 2) is to be determined.

Since the midpoint of a line is given by coordinates;

x = (x1 + x2)/2 and y = (y1 + y2)/2.

It follows that we have;

x = (-3+(-8))/2

x = -11/2

while; y = (8+2)/2

y = 10/2

y = 5.

Ultimately, the midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

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The answer is 6 because you replace c with the 2 (because it says that c equals 2) and add it normally which you get 6

[tex]\cfrac{6}{7}\div \left(-\cfrac{11}{2} \right)\implies \cfrac{6}{7}\cdot \left(-\cfrac{2}{11} \right)\implies -\cfrac{12}{77}[/tex]

Answer:

1.2115/12 times

7=25.179

2.?????????

[tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.

Now, as we know that ln (e) = 1,

In the given expression, [tex]\frac{ln(e)}{4}[/tex], for ln(e) = 1,

The expression becomes: [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex]

Hence, [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.

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The LCM of 1250 and 525 is 26,250.

The HCF of 1250 and 525 is 5.

The factors of a number is the number that perfectly divides another number. For example, a factor of 30 is 3. A prime number is a number that is perfectly divisible by 1 and itself. An example of a prime number is 3. The highest common factor is the highest factor that is common to two or more numbers.

A multiple is the product of a number and another number. For example, the multiple of 3 is 15. This is because 3 multiplied by 5 is 15. The lowest common multiple is the smallest multiple that is common to two or more numbers.

Prime factors of 1250 = 2 x 5 x 5 x 5 x 5

Prime factors of 525 = 3 x 5 x 7

HCF = 5

LCM = 2 x 3 x  5 x 5 x 5 x 5 x 7 = 26,250

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Answer:

49.02

Step-by-step explanation:

Ok, so this is a conversion problem and it wants you to get 45 euros to whatever amount of dollars that equals. So first, you need to get the conversion rate.

1 euro/1.14 dollars

Now, plug in the 43 Euros to the front of the conversion rate

43 euros (1 euro/1.14 dollars)

You want what you start with on the bottom of the conversion factor, so switch the rate around

43 euros (1.14 dollars/1 euro)

Then, multiply what is on top, then divide by what is on the bottom.

49.02 dollars/1=49.02 dollars

The euros go away because they cancelled out.

√3+ √11 is greater than 5 .

We first assume that √3+ √11 is greater than 5. Then we check if our assumption is correct.

So suppose that √3+ √11 > 5

Squaring on both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 14 + 2√33 > 25

Subtracting 14 from both sides,

⇒ 2√33 > 11

Again squaring,

⇒ 132 > 121

This is a true statement. So our assumption that √3+ √11 is greater than 5 is right.

Therefore, √3+ √11 > 5

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Answer:

[tex](5,\, -2)[/tex].

Step-by-step explanation:

For a line segment in a plane, the [tex]x[/tex]-coordinates of the midpoint is the average of the [tex]x\![/tex]-coordinates of the endpoints. Likewise, the [tex]y[/tex]-coordinates of the midpoint is the average of the [tex]y\![/tex] coordinates of the endpoints.

For example, the midpoint of the line segment joining [tex](x_{a},\, y_{a})[/tex] and [tex](x_{b},\, y_{b})[/tex] is:

[tex]\begin{aligned} \left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2}\right)\end{aligned}[/tex].

In this question, [tex]x_{a} = 8[/tex], [tex]x_{b} = 2[/tex], [tex]y_{a} = (-5)[/tex], [tex]y_{b} = 1[/tex]. Thus, the midpoint of the line segment joining the two points would be:

[tex]\begin{aligned} \left(\frac{8 + 2}{2},\, \frac{(-5) + 1}{2}\right)\end{aligned}[/tex].

Simplify to obtain:

[tex]\begin{aligned} \left(5,\, -2\right)\end{aligned}[/tex].

Hence, the midpoint of the line segment joining [tex](8,\, -5)[/tex] and [tex](2,\, 1)[/tex] would be [tex](5,\, -2)[/tex].

The composition of f(x) and g(x) gives:

(f ◦ g) (x) =  x²  + 9x + 20

Here we have the two functions:

f(x) = x² + 5x +6

g(x) = x +2

And we want to find the composition:

(f ◦ g) (x)

The composition means that we need to evaluate f(x) in g(x), so we get:

(f ◦ g) (x) = f( g(x))

Then we will get:

(f ◦ g) (x) = g(x)² + 5*g(x) +6

Now, replacing g(x) we get:

(f ◦ g) (x) = (x + 2)² + 5*(x + 2) + 6

Expanding that, we get:

(x + 2)² + 5*(x + 2) + 6 = x² + 4x + 4 + 5x + 10 + 6 = x²  + 9x + 20

(f ◦ g) (x) =  x²  + 9x + 20

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Attributes shared by rhombuses and rectangles:

Both are quadrilaterals.

Both have their opposing sides equal and parallel.

If a rhombus and a rectangle have the same length and width,

The perimeter of the rhombus equals the sum of the diagonals of the rectangle.

The sum of the diagonals of the rhombus equals the semiperimeter of the rectangle.

The angles of the rhombus equal the angles formed by the diagonals of the rectangle.

The angles formed by the diagonals of the rhombus are all right angles, as are the angles of the rectangle.

The area of the rhombus is one half of the area of the rectangle.

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Answer: 5/3x

Step-by-step explanation:

add 5 to both sides and divide by 3

Step-by-step explanation:

a ratio of 5:5:6 tells us first that there are 5+5+6 = 16 units in all the sides lengths of the triangle.

we don't know how large a single unit is yet, but we know, we have 16 of them.

we also know that all 3 sides together is 32 cm.

and that is another form to bring all side lengths together.

so, we know now that

32 cm = 16 ratio units.

therefore, one ratio unit is 32/16 = 2cm.

therefore, the sides are actually :

2×5 = 10 cm

2×5 = 10 cm

2×6 = 12 cm

so, we have an isoceles triangle (the 2 legs are equally long : 10 cm) with a baseline of 12 cm.

that means the height to the baseline splits the triangle in half (into 2 equal right-angled triangles).

and the height of the main triangle we get via Pythagoras from these smaller triangles :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

10² = (baseline/2)² + height² = 6² + height²

100 = 36 + height²

64 = height²

height = 8

the area of a triangle is

baseline × height / 2

so, in our case the area of the triangle is

12 × 8 / 2 = 12 × 4 = 48 cm²

The required simplification of rational expression is 2c + 3.

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Simplifying the rational expression: 6c² + 9c / 3c

Given a rational expression,

6c² + 9c / 3c

On simplifying, we get,

For numerator, 6c² + 9c: 3c (2c + 3)

For denominator, 3c

Now, 6c² + 9c / 3c = 3c (2c + 3) / 3c

= 2c + 3

There exist no restriction to this problem.

Hence, the required simplification of rational expression is 2c + 3.

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